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Nguyen Tien Dung

Publications and source records attributed to Nguyen Tien Dung.

14 recordsLinked to original sources
arXiv2024

Rates of Fisher information convergence in the central limit theorem for nonlinear statistics

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random variables, we obtain the Fisher information bounds without requiring the finiteness of Poincaré constant. Our method can also be used to bound the Fisher information distance in non-central limit theorems.

math.PR↗
arXiv2024

Non-uniform Berry-Esseen bounds via Malliavin-Stein method

In this paper, we establish non-uniform Berry-Esseen bounds by means of the Malliavin-Stein method. Applications to the multiple Wiener-Itô integrals and the exponential functionals of Brownian motion are given to illustrate the theory.

math.PR↗
arXiv2024

Fisher information bounds and applications to SDEs with small noise

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central limit theorem for the solution of small noise stochastic differential equations and its additive functionals. We also show that the convergence rate is of optimal order.

math.PR↗
arXiv2021

Rates of convergence in the CLT for nonlinear statistics under relaxed moment conditions

This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of order $2+δ\in(2,3];$ (ii) nonlinear statistics with vanishing third moment and finite absolute moment of order $3+δ\in(3,4].$ When applied to specific examples, these rates are of the optimal order $O(n^{-\fracδ{2}})$ and $O(n^{-\frac{1+δ}{2}}).$ Our proof are based on the covariance identify formula and simple observations about the solution of Stein's equation.

math.PR↗
arXiv2021

On the density of nonlinear statistics

In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is provided.

math.PR↗
arXiv2019

Gaussian lower bounds for the density via Malliavin calculus

In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables. This new representation is particularly useful for finding lower bounds for the density.

math.PR↗
arXiv2018

Explicit rates of convergence in the multivariate CLT for nonlinear statistics

We investigate the multivariate central limit theorem for nonlinear statistics by means of Stein's method and Slepian's smart path interpolation method. Based on certain difference operators in theory of concentration inequalities, we obtain two explicit bounds for the rate of convergence. Applications to Rademacher functionals, the runs and quadratic forms are provided as well.

math.PR↗
arXiv2018

Poisson and normal approximations for the measurable functions of independent random variables

In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in theory of concentration inequalities to obtain explicit bounds on Wasserstein, Kolmogorov and total variation distances. When restricted to the functions of a finite number of independent random variables, our method provides new bounds in the normal approximation. Meanwhile, our bounds in Poisson approximation are first to obtain explicitly.

math.PR↗